Publications related to Differential anaysis

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Manufacturing-Enabled Tunability of Linear and Nonlinear Epsilon-Near-Zero Properties in Indium Tin Oxide Nanofilms

Jiaye Wu, Qian Li, Xuanyi Liu

Epsilon-near-zero (ENZ) materialshave attracted great interestdue to their exotic linear and nonlinear responses, which makes itsignificant to tune ENZ wavelengths for wavelength-dependent applications.However, studies to achieve tunability in a wide spect ...

AMER CHEMICAL SOC2023

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Maria Colombo, Silja Noëmi Aline Haffter

We consider the defocusing nonlinear wave equation ❑u D jujp ⠀1u in R3 ⠂ & UOELIG;0; 1/. We prove that for any initial datum with a scaling-subcritical norm bounded by M0 the equation is globally well-posed for p D 5 C i, where i 2 .0; ...

MATHEMATICAL SCIENCE PUBL2023

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

Espen Sande

We present outlier-free isogeometric Galerkin discretizations of eigenvalue problems related to the biharmonic and the polyharmonic operator in the univariate setting. These are Galerkin discretizations in certain spline subspaces that provide accurate app ...

Lausanne2023

Stability of Image-Reconstruction Algorithms

Michaël Unser, Sebastian Jonas Neumayer, Pol del Aguila Pla

Robustness and stability of image-reconstruction algorithms have recently come under scrutiny. Their importance to medical imaging cannot be overstated. We review the known results for the topical variational regularization strategies ( ℓ2 and ℓ1 regulariz ...

2023

Detecting whether a stochastic process is finitely expressed in a basis

Victor Panaretos, Neda Mohammadi Jouzdani

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Continuous-variable neural network quantum states and the quantum rotor model

Giuseppe Carleo

We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunc ...

SPRINGERNATURE2023

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Fabio Nobile, Juan Pablo Madrigal Cianci

In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo(ML-MCMC) algorithms based on independent Metropolis--Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving ...

2023

Incremental Learning in Diagonal Linear Networks

Raphaël Jean Berthier

Diagonal linear networks (DLNs) are a toy simplification of artificial neural networks; they consist in a quadratic reparametrization of linear regression inducing a sparse implicit regularization. In this paper, we describe the trajectory of the gradient ...

Brookline2023

Density Estimation In Rkhs With Application To Korobov Spaces In High Dimensions

Fabio Nobile, Yoshihito Kazashi

A kernel method for estimating a probability density function from an independent and identically distributed sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined b ...

SIAM PUBLICATIONS2023

Differential anaysis

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Moments of the number of points in a bounded set for number field lattices

Manufacturing-Enabled Tunability of Linear and Nonlinear Epsilon-Near-Zero Properties in Indium Tin Oxide Nanofilms

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

Stability of Image-Reconstruction Algorithms

Detecting whether a stochastic process is finitely expressed in a basis

Continuous-variable neural network quantum states and the quantum rotor model

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Incremental Learning in Diagonal Linear Networks

Density Estimation In Rkhs With Application To Korobov Spaces In High Dimensions

Moments of the number of points in a bounded set for number field lattices

Manufacturing-Enabled Tunability of Linear and Nonlinear Epsilon-Near-Zero Properties in Indium Tin Oxide Nanofilms

Detecting whether a stochastic process is finitely expressed in a basis

Density Estimation In Rkhs With Application To Korobov Spaces In High Dimensions

Incremental Learning in Diagonal Linear Networks

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

Stability of Image-Reconstruction Algorithms

Continuous-variable neural network quantum states and the quantum rotor model

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems